machine-learning-ex2_1

最新推荐文章于 2019-06-16 22:41:44 发布

原创最新推荐文章于 2019-06-16 22:41:44 发布 · 906 阅读

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#machine-learning #one

本文通过一个具体实例展示了如何使用逻辑回归进行二分类预测问题的解决过程。从数据加载、可视化到成本函数计算、梯度下降优化直至决策边界绘制，并最终评估模型准确性。

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%% Load Data

data = load('ex2data1.txt');
X = data(:, [1, 2]); y = data(:, 3);

%%Plotting

plotData(X, y);

function plotData(X, y)
figure;hold on;
pos=find(y==1);neg=find(y==0);
plot(X(pos,1),X(pos,2),'k+','LineWidth',2,...
    'MarkerSize',7);
plot(X(neg,1),X(neg,2),'ko','MarkerFaceColor','y',...
    'MarkerSize',7);
hold off;

end

hold on;

xlabel('Exam 1 score')
ylabel('Exam 2 score')

legend('Admitted', 'Not admitted')
hold off;

%%Compute Cost and Gradient

[m, n] = size(X);

X = [ones(m, 1) X];

initial_theta = zeros(n + 1, 1);

[cost, grad] = costFunction(initial_theta, X, y);

function [J, grad] = costFunction(theta, X, y)
m = length(y);
J = 0;
grad = zeros(size(theta));
sig=sigmoid(X * theta);
J=-(1/m)*sum(y' * log(sig)+ (1-y') * log(1- sig));
grad=(1/m )* (X'* (sig-y));
end

fprintf('Cost at initial theta (zeros): %f\n', cost);
fprintf('Gradient at initial theta (zeros): \n');
fprintf(' %f \n', grad);
%%Optimizing using fminunc

options = optimset('GradObj', 'on', 'MaxIter', 400);

[theta, cost] = ...
fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);

fprintf('Cost at theta found by fminunc: %f\n', cost);

fprintf('theta: \n');
fprintf(' %f \n', theta);

plotDecisionBoundary(theta, X, y);

function plotDecisionBoundary(theta, X, y)
plotData(X(:,2:3), y);
hold on
if size(X, 2) <= 3
    plot_x = [min(X(:,2))-2,  max(X(:,2))+2];
    plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));
    plot(plot_x, plot_y)
    legend('Admitted', 'Not admitted', 'Decision Boundary')
    axis([30, 100, 30, 100])
else
    u = linspace(-1, 1.5, 50);
    v = linspace(-1, 1.5, 50);
    z = zeros(length(u), length(v));
    for i = 1:length(u)
        for j = 1:length(v)
            z(i,j) = mapFeature(u(i), v(j))*theta;
        end
    end
    z = z';
   contour(u, v, z, [0, 0], 'LineWidth', 2)
end
hold off

end

hold on;

xlabel('Exam 1 score')

ylabel('Exam 2 score')
legend('Admitted', 'Not admitted')
hold off;

%%Predict and Accuracies

prob = sigmoid([1 45 85] * theta);

function g = sigmoid(z)
g = zeros(size(z));
g=1./(1+exp(-z));
end

fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
'probability of %f\n\n'], prob);

p = predict(theta, X);

function p = predict(theta, X)
m = size(X, 1);
p = zeros(m, 1);
sig=sigmoid(X * theta);
for iter=1:m
    if sig(iter)>=0.5
        p(iter)=1;
    else 
        p(iter)=0;
    end;
end;
end

fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
fprintf('\nProgram paused. Press enter to continue.\n');
pause;